/* @(#)e_log10.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include "math.h"
#include "float.h"
#include "k_log.h"

static const double
two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln2hi    =  1.44269504072144627571e+00, /* 0x3ff71547, 0x65200000 */
ivln2lo    =  1.67517131648865118353e-10; /* 0x3de705fc, 0x2eefa200 */

static const double zero   =  0.0;
static volatile double vzero = 0.0;

double
__ieee754_log2(double x)
{
    double f,hfsq,hi,lo,r,val_hi,val_lo,w,y;
    int i,k,hx;
    unsigned int lx;

    EXTRACT_WORDS(hx,lx,x);

    k=0;
    if (hx < 0x00100000) {            /* x < 2**-1022  */
        if (((hx&0x7fffffff)|lx)==0)
        return -two54/vzero;        /* log(+-0)=-inf */
        if (hx<0) return (x-x)/zero;    /* log(-#) = NaN */ /*lint !e414*/
        k -= 54; x *= two54; /* subnormal number, scale up x */
        GET_HIGH_WORD(hx,x);
    }
    if (hx >= 0x7ff00000) return x+x;
    if (hx == 0x3ff00000 && lx == 0)
        return zero;            /* log(1) = +0 */
    k += (hx>>20)-1023;
    hx &= 0x000fffff;
    i = (hx+0x95f64)&0x100000;
    SET_HIGH_WORD(x,hx|(i^0x3ff00000));    /* normalize x or x/2 */
    k += (i>>20);
    y = (double)k;
    f = x - 1.0;
    hfsq = 0.5*f*f;
    r = k_log1p(f);

    /*
     * f-hfsq must (for args near 1) be evaluated in extra precision
     * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
     * This is fairly efficient since f-hfsq only depends on f, so can
     * be evaluated in parallel with R.  Not combining hfsq with R also
     * keeps R small (though not as small as a true `lo' term would be),
     * so that extra precision is not needed for terms involving R.
     *
     * Compiler bugs involving extra precision used to break Dekker's
     * theorem for spitting f-hfsq as hi+lo, unless double_t was used
     * or the multi-precision calculations were avoided when double_t
     * has extra precision.  These problems are now automatically
     * avoided as a side effect of the optimization of combining the
     * Dekker splitting step with the clear-low-bits step.
     *
     * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
     * precision to avoid a very large cancellation when x is very near
     * these values.  Unlike the above cancellations, this problem is
     * specific to base 2.  It is strange that adding +-1 is so much
     * harder than adding +-ln2 or +-log10_2.
     *
     * This uses Dekker's theorem to normalize y+val_hi, so the
     * compiler bugs are back in some configurations, sigh.  And I
     * don't want to used double_t to avoid them, since that gives a
     * pessimization and the support for avoiding the pessimization
     * is not yet available.
     *
     * The multi-precision calculations for the multiplications are
     * routine.
     */
    hi = f - hfsq;
    SET_LOW_WORD(hi,0);
    lo = (f - hi) - hfsq + r;
    val_hi = hi*ivln2hi;
    val_lo = (lo+hi)*ivln2lo + lo*ivln2hi;

    /* spadd(val_hi, val_lo, y), except for not using double_t: */
    w = y + val_hi;
    val_lo += (y - w) + val_hi;
    val_hi = w;

    return val_lo + val_hi;
}

double log2(double x)
{
    return __ieee754_log2(x);
}

